Radio! AKICOLJ

Say that I want to listen to something on iPlayer. I can download it, and it will stay on my computer for a period of time before vanishing forever. But say that I want to keep it permanently. There is a radio-cassette player behind me, so I could use that, but I know that it can be done with the computer* - but how?

*Not least because it has kindly been done for me in the past, but I am a grown-up so I ought to do it myself now I have reliable broadband.